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||             Electronic Proceedings of the Tenth Annual             ||
||  International Conference on Technology in Collegiate Mathematics  ||
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CONTRIBUTED PAPER: 10-C9

Animated Demonstrations for Multivariable Calculus

John F. Putz
Mathematics and Computer Science Department
Alma College
Alma, MI  48801
Phone: (517) 463-7253     
Fax: (517) 463-7277E-mail: putz@alma.edu

ABSTRACT

With the ability of computer algebra systems to graph surfaces in 
three dimensions, came a major leap in our capacity to convey the 
ideas of multivariable calculus.  Their facility for animation is 
the next significant stride.  Of all the methods I have tried, 
animated demonstrations have been the most effective, particularly 
for:  quadric surfaces; level curves and level surfaces; velocity 
and acceleration vectors; and directional derivative and gradient 
vector.  In this paper, I share ten animated demonstrations that 
I have written using Maple V Release 4 to teach these topics.